Shared up-the-wall vent for three fixtures?

I'm turning a 5x9 porch (over shallow crawl space) into a three-quarter bath with lavatory on east wall, shower across south end, toilet on west wall. I'd like to bring the lavatory drain and shower drain together into a 2" wye, then that wye into the two-inch wye neck of a 3x3x2 fitting that will aim toward my 4" main drainline in the basement. The lav/shower drain would enter the 3" main line a foot or so downstream of the closet bend. All the drains will be horizontal (lying under the subfloor) with proper 1/4" drop per foot until the 3" drops vertically into the 4" basement plumbing. My question is regarding venting. With such short drain lines (nothing more than five feet apart) can I get by with one 2" vent in a wall (either for the lavatory or toilet) serving all three fixtures, or do I need separate vents for each? The vent could go straight up through the roof on either the lav wall or the toilet wall. In other words, do I need three pipes up a wall or will the one 2" vent pipe that joins the drain under the floor be sufficient to vent all three fixtures? I know it is OK to run separate vents for each fixture upward to join one large through-the-roof vent above the ceiling; what I'm asking is whether I can avoid two of those three pipes going up a wall. Is this at all clear what I'm explaining? FWIW, there are no codes or inspections or permits required; I'm in an area where no one officially cares, but I try to do work that would meet typical codes. Thanks for any advice.

VEnt requirements have NOTHING to do with how close the fixtures are to each other. IT depends on HOW the piping is arranged. From YOUR description, and that is all we have to go by, it is a proper installation, IF you actually install it the way you indicate. Depending on the actual space limitations, however, I might do it completely differently.

I was just trying to get a picture of what u were saying...as for what will work...u need to take advice from Hj , or Wally, they are the pros...I just thought a illustration could help with discussion...